Temporal Evolution of Mortality Indicators

Abstract

In Spain, as in other developed countries, there have been significant changes in mortality patterns during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, though the robustness of this indicator prevents these changes from being of the same order as those for the probability of death, q xt . If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study.These indicators are applied to Spanish mortality data for the period 1981-2008, for the age range 0 to 99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely the Lee-Carter model (Lee and Carter, 1992;Brouhns et al., 2002;Debón et al., 2008b). With the aim of incorporating the uncertainty measures suggested by Pedroza (2006) into predictions, confidence intervals are obtained for these predictions. These intervals can be calculated using the methodology which Lee and Carter apply in their original article for expected lifetime confidence intervals, but they only take into account the error in the prediction of the mortality index k t obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, as used in Koissi et al. (2006), permitting the combination of all sources of uncertainty.

Mortality forecasting in Colombia from abridged life tables by sex

“…In addition, diagnostic checks on the fitted model by plotting standardized deviance residuals were carried out as sole use of goodness of fit measures is not a satisfactory diagnostic indicator in our experience ( Debón et al 2008 ; Debón et al 2012 ). In the graphical analysis of these residuals, their behavior with respect to age, period, and cohort was evaluated through dispersion plots.…”

“…This group includes birth and fertility indicators, age-specific mortality rates, and life expectancy, among others. Another group of mortality indicators summarizes the associations between health inequalities and socioeconomic indicators, such as the modal age at death, the Lorenz mortality curve, and the Gini mortality index ( Debón et al 2012 ). Life expectancy at age x ( e x ): Life expectancy represents the average number of years left to live for survivors at age x if existing mortality conditions prevail, the expression is: where T xt corresponds to the remaining lifetime for the individuals of a generation from age x to its complete extinction and l xt the number of survivors at the same age x .…”

Characterization of between-group inequality of longevity in European Union countries

“…In order to analyse the behavior of mortality over age and time, both trend indicators and measures to quantify their variability were selected. For each year studied we calculate trend mortality indicators including infant mortality, modal age at death, life expectancy and variability mortality indicators such as Gini index and conditional standard deviation; more details are provided in Debón et al (2012).…”

“…In keeping with Keyfitz's idea (Keyfitz and Caswell, 2005) that everybody dies prematurely, Mitra (1978) developed the measure the average life expectancy lost due to death and Shkolnikov et al (2003) initiated a new direction by means of the Gini Index. As Debón et al (2012) proposed, the contribution of a particular age group x to the life expectancy at birth, e 0t = T 0t l 0t , can be seen as the balance between the contribution to the numerator (years lived) and the denominator (population). Therefore, the proportion dead of the life table stationary population at age x can be obtained by…”

Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model

“…It is also essential to have an appropriate set of indicators for studying these phenomena, including life expectancy, the Gini index, and the modal age at death [ 6 , 7 ]. All of these indicators can be projected using the predictions of annual age-specific mortality probabilities, , obtained from different methodologies, which are based, in this paper, on Lee-Carter models.…”